Drafted to the NHL by the Islanders 65th overall in the 1972 NHL Amateur Draft following a good junior career with the Rosemont National, the Quebec Remparts and the Verdun Maple Leafs, Grenier enjoyed his first NHL action in 1972-73. He played in 10 games, scoring once and adding one assist. Unfortunately for him, if NHL action came early in his pro career, it just never happened again. He played in the American Hockey League, the Central Hockey League and the North American Hockey League before major league became a reality again, as he joined the Quebec Nordiques. He split the season between the World Hockey Association's Nordiques and their NAHL farm team, the Maine Nordiques and didn't do bad in the WHA, with 11 goals and 9 assists in 34 games. That was not sufficient however to secur